Gun-toting whites prevent blacks from fleeing their Mississippi town during a flood in this musical. Photo: Erin Baiano

LCT3 may be the newest and most intimate unit of Lincoln Center Theater, but its shows certainly don’t think small. “On the Levee,” which opened last night, tackles no less than race, class and father-son relationships against a quasi-mythical backdrop: the great Mississippi flood of 1927.

The action is set in Greenville, Miss., where the white establishment, afraid to lose its workforce, prevented thousands of African-Americans from leaving their devastated neighborhood.

Playwright Marcus Gardley approaches his big themes by zooming in on two interconnected sets of characters, one white and one black. They’re linked by Joe Gooden (Dion Graham), who’s employed by the local power family, the Percys. Patriarch LeRoy Percy (Michael Siberry) lords it over the entire region and also bullies his idealistic son, Will (Seth Numrich). Meanwhile, Joe’s son, the smooth-talking James (Amari Cheatom), runs the local juke joint.

Gardley and director Lear DeBessonet lean on fairly conventional narrative themes such as jealousy and forbidden love, but they also use videos and shadow puppets designed by artist Kara Walker, as well as songs by Todd Almond that are infused with blues, gospel and honky-tonk.

At first, those are performed in context — at a party, at James’ club — as befits a show billed as “a play with music.” But by the third act, the songs are used to develop plot and character, as in a traditional musical. (The creative team has mentioned “Showboat” as one of its influences.)

It’s an interesting choice — especially when you have powerhouse singers such as Chuck Cooper (“The Life”) in your cast — but it also feels awkward, as if the show were unsure of its direction.

Not surprisingly, this waffling causes “On the Levee” to lose steam. The characters busy themselves on a set dominated by sandbags, yet their plight feels less and less urgent — until a coda that leaves the audience uncomfortable. It’s a provocative move, although perhaps sapped of its impact because it comes out of the blue.

“On the Levee” flirts with emotions and even sentimentality but doesn’t fully commit to them — none of the live action is as graphic or as powerfully engaging as Walker’s little vignettes.

Tellingly, the director recently said that “tears are definitely not the answer.” The show is ambitious but it holds us at arm’s length, and it’s the audience that ends up high and dry.